Splitter Theorems for Cubic Graphs

Let k g be the class of k connected cubic graphs of girth at least g For several choices of k and g we determine a set Ok g of graph operations for which if G and H are graphs in k g G H and G contains H topologically then some operation in Ok g can be applied to G to result in a smaller graph G in k g such that on one hand G is contained in G topologically and on the other hand G contains H topologically Research partially supported by NSF grant DMS and AFOSR grant F